Calculating the freezing point of seawater

Objective

The freezing point of sea water depends on salinity and pressure. Millero and Leung (Millero & Leung 1976) give a formula for the calculation of this temperature. Here a function is given to compute the freezing point in °C for seawater at given values of practical salinity and pressure in decibars.

Equation

The adopted equation given in the UNESCO handbook ‘Algorithms for computation of fundamental properties of seawater’ (UNESCO 1983) is:

In this equation t_f is the freezing point in °C, S the salinity in PSS-78 and p the pressure in decibars. The equation is valid in the practical salinity range of 4 to 40 at atmospheric pressure. Measurements at elevated pressures showed no significant dependence of the pressure coefficient on salinity in the range of 27 to 35 (Fujino et al. 1974). The estimated error to pressure of 500 decibars is 0.003°C .

Algorithm

The below algorithm in object Pascal is equal to the original Fortran code (UNESCO 1983). For given values of salinity and pressure the freezing point of sewater is returned.

Function TF (S, P : Double): Double;
// FUNCTION TO COMPUTE THE FREEZING POINT OF SEAWATER
// REFERENCE: UNESCO TECH. PAPERS IN THE MARINE SCIENCE NO. 28. 1978
// EIGHTH JPOTS
// ANNEX 6 FREEZING POINT OF SEAWATER F.J. MILLERO PP.29-35.
// ----------------------------------------------------------
// UNITS:
//   PRESSURE     P   DECIBARS
//   SALINITY     S   PSS-78
//   TEMPERATURE  TF  DEGREES CELSIUS FREEZING PT.
// ----------------------------------------------------------
// CHECKVALUE:
//   TF=-2.588567 DEG C for S=40.0, P=500.0 DECIBARS
// ----------------------------------------------------------
// Original fortran code is found in:
//   UNESCO technical papers in marine science 44 (1983) -
//   'Algorithms for computation of fundamental properties of seawater'
// ----------------------------------------------------------
// Translated to object pascal by:
//   Dr. Jan Schulz, 20. May 2008, www.code10.info
Begin
  TF := (-0.0575 + 1.710523E-3 * Sqrt (Abs (S)) - 2.154996E-4 * S) * S - 7.53E-4 * P;
end;
 

Literature

Fujino K., Lewis E.L., Perkin R.G. (1974): The freezing point of seawater at pressures up to 100 bars. Journal of Geophysic Research 79:1792-1797.

Millero F.J., Leung W.H. (1976): The thermodynamics of seawater at one atmosphere. American Journal of Science 276:1035-1077.

UNESCO (1983): Algorithms for computation of fundamental properties of seawater. UNESCO technical papers in marine science 44:1-55.